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Direction sense with diagonal moves: find the straight-line distance from the start Radha moves 7 km South-East → 14 km West → 7 km North-West → 4 km East. Compute her net displacement from the starting point. Choose the correct value.

Difficulty: Medium

Correct Answer: 10 km

Explanation:

Vector components

  • SE 7 km = ( +7/√2, −7/√2 )
  • West 14 km = ( −14, 0 )
  • NW 7 km = ( −7/√2, +7/√2 )
  • East 4 km = ( +4, 0 )

Sum components x = 7/√2 − 14 − 7/√2 + 4 = −14 + 4 = −10 km y = −7/√2 + 7/√2 = 0 km

Distance |Δ| = √( (−10)² + 0² ) = 10 km (towards West).

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